Homework 4 1 combining functions answers

Find and simplify the functions (g − f)(x) and (g f)(x), given f(x) = x − 1 and g(x) = x2 − 1. Are they the same function? Begin by writing the general form, and then substitute the given functions. No, the functions are not the same.

Begin by writing the general form, and then substitute the given functions. No, the functions are not the same. Note: For (g f)(x), the condition x ≠ 1 is necessary because when x = 1, the denominator is equal to 0, which makes the function undefined.

Example 2 Given f (x) = 2 +3x−x2 f ( x) = 2 + 3 x − x 2 and g(x) = 2x −1 g ( x) = 2 x − 1 evaluate each of the following. These are the same functions that we used in the first set of examples and we’ve already done this part there so we won’t redo all the work here.

When the output of one function is used as the input of another, we call the entire operation a composition of functions. For any input x and functions f and g, this action defines a composite function, which we write as f ∘ g such that (f ∘ g)(x) = f(g(x))